Dynamic Euler-Bernoulli beam equation: classification and reductions

DOI10.1155/2015/520491zbMath1394.74085OpenAlexW1685461303WikidataQ59118841 ScholiaQ59118841MaRDI QIDQ1665907

Y. Aharonov

Publication date: 27 August 2018

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2015/520491

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Geometric theory, characteristics, transformations in context of PDEs (35A30) Initial-boundary value problems for higher-order hyperbolic equations (35L35) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (5)

Symmetry methods for a hyperbolic model for a class of populations ⋮ Analysis of the lumped mass model for the cantilever beam subject to Grob's swelling pressure ⋮ Parametric Solutions to a Static Fourth-Order Euler–Bernoulli Beam Equation in Terms of Lamé Functions ⋮ Exact general solution and first integrals of a remarkable static Euler-Bernoulli beam equation ⋮ A new analytical method for spherical thin shells' axisymmetric vibrations

Cites Work

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• Euler-Bernoulli beams from a symmetry standpoint-characterization of equivalent equations
• Equivalence transformations of the Euler-Bernoulli equation
• Invariant boundary value problems for a fourth-order dynamic Euler-Bernoulli beam equation
• The equivalence problem for the Euler–Bernoulli beam equation via Cartan's method
• Isospectral Euler-Bernoulli beams with continuous density and rigidity functions
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• Symmetries and integrability of a fourth-order Euler–Bernoulli beam equation

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